diff --git a/sympy/core/power.py b/sympy/core/power.py
index 13b4b560f7..415333bfe2 100644
--- a/sympy/core/power.py
+++ b/sympy/core/power.py
@@ -449,6 +449,8 @@ def _eval_is_positive(self):
                     return False
             if self.exp.is_imaginary:
                 return log(self.base).is_imaginary
+        if self.base.is_zero and self.exp.is_real and not self.exp.is_zero:
+            return False
 
     def _eval_is_negative(self):
         if self.base.is_negative:
